## Integral minimal models for binary forms

#### When/Where:

June 5, 2015, 1:55 — 2:45pm at LIT 368.

#### Abstract:

Let $$K$$ be a number field, $$\mathfrak O_K$$ its ring of integers, and $$f \in \mathfrak O_K [x, z]$$ a degree $$n$$ binary form.

We devise an algorithm which accomplishes the following:

1. finds a binary form $$f^\prime$$, $$\bar K$$-equivalent to $$f$$, with minimal height $$h (f)$$ (i.e., smallest coefficients),
2. enumerates all twists $$g \in O_K [x, z]$$ of $$f$$ with $$h (g) \leq h(f)$$.

Our methods rely and  extend previous results of Hermite, Julia, Cremona, and Stoll.